What does it mean for a set to be "closed"?(1 point) Responses An expression belonging to a closed set cannot be used to create an expression that is not of that set. An expression belonging to a clo

Answer 1

In mathematics, a set is said to be "closed" with respect to a particular operation if performing that operation on members of the set always produces a result that is also a member of the set.

For example:

• A set \( S \) is closed under addition if for any elements \( a \) and \( b \) in \( S \), the sum \( a + b \) is also in \( S \).
• A set is closed under multiplication if for any elements \( a \) and \( b \) in the set, the product \( a \cdot b \) is also in the set.

In topology, a set is closed if it contains all its limit points, meaning that if a sequence of points in the set converges to a point, that point is also in the set.

So to summarize, a set being "closed" implies that the operations of interest do not produce results outside the set.